Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-16.1-a
Conductor 16.1
Rank not recorded

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Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 16.1-a over \(\Q(\sqrt{17}) \)

Isogeny class 16.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -38 a - 77\) , \( -268 a - 444\bigr] \)
16.1-a2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \)
16.1-a3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4\) , \( a - 4\bigr] \)
16.1-a4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 40 a - 116\) , \( 229 a - 596\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph